Question

Bill will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $59.98 and costs an additional $0.13 per mile driven. Thesecond plan has an initial fee of $71.98 and costs an additional $0.11 per mile driven. How many miles would Bill need to drive for the two plans to cost thesame? __ miles

Answer 1

The number of miles Bill would have driven for the two plans to cost the same is;

`600\text{ miles}`

Step-by-step explanation:

Given that He can choose one of two plans.

Let C represent the cost and x represent the miles driven.

Plan 1;

an initial fee of $59.98 and costs an additional $0.13 per mile driven.

`C_1=59.98+0.13x\text{ --------1}`

Plan 2;

an initial fee of $71.98 and costs an additional $0.11 per mile driven.

`C_2=71.98+0.11x\text{ -----------2}`

For the two plans to cost the same;

`C_1=C_2`

equating equation 1 to equation 2;

`\begin{gathered} 59.98+0.13x=71.98+0.11x \\ 0.13x-0.11x=71.98-59.98 \\ 0.02x=12 \\ x=(12)/(0.02) \\ x=600 \end{gathered}`

Therefore, the number of miles Bill would have driven for the two plans to cost the same is;

`600\text{ miles}`